Asymptotically Optimal Tests for Single-Index Restrictions with a Focus on Average Partial Effects

This paper proposes an asymptotically optimal specification test of single-index models against alternatives that lead to inconsistent estimates of a covariate’s average partial effect. The proposed tests are relevant when a researcher is concerned about a potential violation of the single-index restriction only to the extent that the estimated average partial effects suffer from a nontrivial bias due to the misspecifcation. Using a pseudo-norm of average partial effects deviation and drawing on the minimax approach, we find a nice characterization of the least favorable local alternatives associated with misspecified average partial effects as a single direction of Pitman local alternatives. Based on this characterization, we define an asymptotic optimal test to be a semiparametrically efficient test that tests the significance of the least favorable direction in an augmented regression formulation, and propose such a one that is asymptotically distribution-free, with asymptotic critical values available from the X 2/1 table. The testing procedure can be easily modified when one wants to consider average partial effects with respect to binary covariates or multivariate average partial effects.Average Partial Effects, Omnibus tests, Optimal tests, Semi- parametric Efficiency, Efficient Score

Observables and Microscopic Entropy of Higher Spin Black Holes

In the context of recently proposed holographic dualities between higher spin theories in AdS3 and 1+1-dimensional CFTs with W-symmetry algebras, we revisit the definition of higher spin black hole thermodynamics and the dictionary between bulk fields and dual CFT operators. We build a canonical formalism based on three ingredients: a gauge-invariant definition of conserved charges and chemical potentials in the presence of higher spin black holes, a canonical definition of entropy in the bulk, and a bulk-to-boundary dictionary aligned with the asymptotic symmetry algebra. We show that our canonical formalism shares the same formal structure as the so-called holomorphic formalism, but differs in the definition of charges and chemical potentials and in the bulk-to-boundary dictionary. Most importantly, we show that it admits a consistent CFT interpretation. We discuss the spin-2 and spin-3 cases in detail and generalize our construction to theories based on the hs[\lambda] algebra, and on the sl(N,R) algebra for any choice of sl(2,R) embedding.Comment: 47 pages, references added, published versio